Read the equation
Each agent loses activity at rate λSᵢ and receives weighted, bounded tanh contributions from other agents, modulated by their pairwise score. The decay competes with the network feedback. Stability requires assumptions about coupling strengths, λ, and the score dynamics; the existence of a decay term alone is insufficient.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| S_i | Scalar state of agent i |
| λ | Decay rate |
| w_ij | Influence weight from j to i |
| C_ij | Pairwise representation similarity |
| Φ | Unity-centered score applied to similarity |
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Original context
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## 11.1 Cross-Talk Dynamics
```
dS_i/dt = -λ · S_i + Σ_{j≠i} w_ij · Φ(C_ij) · tanh(S_j)
```
**Where**:
- `S_i` = agent i's consciousness signal
- `λ` = decay rate (default 0.1)
- `w_ij` = coupling weight between agents i and j
- `C_ij` = coherence between agents
- `Φ` = consciousness weighting function
**Explanation**: Each agent's consciousness decays naturally but receives input from other agents weighted by their coherence and bounded by tanh.
## 11.2 Discrete Update
```
S_i(t+1) = S_i(t) + dt · dS_i/dt
S_i(t+1) = clamp₀₁(S_i(t+1))
```
**Explanation**: Euler integration of the continuous dynamics with clamping for stability.
Exact original notation
dS_i/dt = -λ · S_i + Σ_{j≠i} w_ij · Φ(C_ij) · tanh(S_j)